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Future Blog Post

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Published: January 01, 2199

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Blog Post number 4

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Published: August 14, 2015

This is a sample blog post. Lorem ipsum I can’t remember the rest of lorem ipsum and don’t have an internet connection right now. Testing testing testing this blog post. Blog posts are cool.

Blog Post number 3

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Published: August 14, 2014

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Blog Post number 2

less than 1 minute read

Published: August 14, 2013

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Blog Post number 1

less than 1 minute read

Published: August 14, 2012

This is a sample blog post. Lorem ipsum I can’t remember the rest of lorem ipsum and don’t have an internet connection right now. Testing testing testing this blog post. Blog posts are cool.

notes

The note is based on Chapter 2,3,5,6 of Stein’s book Fourier Analysis: An Introduction, which is an elegant book for undergraduates majoring in mathematics, especially the beginners with basic knowledge of Mathematical Analysis. I read the book after my first year of math learning and it really invoked my interest of further analysis, because you can easily find its applications in solving wave equations and heat equations by just using Fourier transformation on those equations, what a useful tool!

A note of Differential Equations

The note is my handwritten note of Introduction to Differential Equations, a required lesson of students in SMS. The lesson contains two part, basic ODE theory and classical PDE theory. For ODE part, I think it’s important to master the solutions of some fundamental equations, continuation theorem(you can try to understand it from a topological view), Lyapunov stability and S-L theory(very important in PDE). For PDE part, I think it’s important to master the techniques of variables separation, energy estimation(globally) and maxinum modulus principle. Though the content is huge, you can understand most of it not so painful if you persist to attend the class and take notes.

A note of Topology

The note is my handwritten note of Topology(H), a very valuable lesson from my point of view. Its content is comprehensive, ranging from point set topology to basic algebraic topology(though Prof.Wang thought it should be called “topological invariant”), even some topics in geometric topology and combinatorial topology. In my opinion, the knowledge about pset topo which has to do with analysis does benefit me a lot, since it can really help you to understand the “skills” in analysis.

A note of Real Analysis

The note is based on some chapters of both Stein’s book Real Analysis and Folland’s book Real Analysis. Both are classical textbook for learners of this discipline. In my opinion, Stein’s book are much more friendly for beginer, but if someone wants to get a broader understanding of real analysis, I personally think it will be a better choice to read Folland’s book after reading the first three chapters of Stein’s book.

A note of Complex Analysis

The note is my padnote of Complex Analysis, written for recording what I have learnt. As for the textbook, I mainly referred to the first seven chapters of 复变函数 written by 史济怀&刘太顺 and the fourth and fifth chapters of Complex analysis written by Stein. The theory, mainly about the holomorphic functions, manifest an interesting world of analysis different from what I had learnt. Maybe I can have a deeper understanding after learning Riemann Surface.